Anshu, Swati and Rajni can finish a work in 4 days if they work together. However, Anshu alone will take 9 days to complete the work, and Swati alone will complete the work in 12 days. How many days will Rajni alone take to complete the work?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 09 Dec 2022 Shift 1)

Answer 1

Given:

Time taken by all to complete the work = 4 days

Time taken by Anshu to complete the work = 9 days

Time taken by Swati to complete the work = 12 days

Concept used:

Anshu's 1 day work = \(1 \over 9\)

Swati's 1 day work = \(1 \over 12\)

Anshu's, Swati's and Rajni's one day work together = \(1 \over 4\)

Calculation:

Let's denote the fraction of the work completed per day by Anshu, Swati, and Rajni as "a", "s", and "r", respectively.

When they work together, they complete the work in 4 days, so we can write:

4(a + s + r) = 1

We also know that Anshu alone will take 9 days to complete the work, so we can write:

9a = 1

Similarly, Swati alone will complete the work in 12 days, so we can write:

12s = 1

To find the time taken by Rajni alone to complete the work, we need to solve for "r". We can start by rearranging the first equation to get:

a + s + r = \(\frac{1}{4}\)

Then, we can substitute the values of "a" and "s" from the second and third equations, respectively:

\(\frac{1}{9}\) + \(\frac{1}{12}\) + r = \(\frac{1}{4}\)

Simplifying this equation, we get:

⇒\(\frac{7}{36}\) + r = \(\frac{1}{4}\)

⇒r = \(\frac{1}{4}-\frac{7}{36}\)

⇒r = \(\frac{1}{18}\)

∴ Rajni alone will take 18 days to complete the work.